8 Permanent-MagnetAssisted Reluctance Synchronous Starter/ Alternators for Electric Hybrid Vehicles 8.1 8.2 8.3 Introduction 8-1 Topologies of PM-RSM 8-3 Finite Element Analysis 8-5 Flux Distribution • The d–q Inductances • The Cogging Torque • Core Losses Computation by FEM 8.4 8.5 The d–q Model of PM-RSM 8-12 Steady-State Operation at No Load and Symmetric Short-Circuit 8-19 Generator No-Load • Symmetrical Short-Circuit 8.6 Design Aspects for Wide Speed Range Constant Power Operation 8.7 Power Electronics for PM-RSM for Automotive Applications 8.8 Control of PM-RSM for EHV 8.9 State Observers without Signal Injection for Motion Sensorless Control 8.10 Signal Injection Rotor Position Observers 8.11 Initial and Low Speed Rotor Position Tracking 8.12 Summary References 8-21 8-27 8-30 8-32 8-34 8-34 8-39 8-41 8.1 Introduction The permanent-magnet-assisted reluctance synchronous machine (PM-RSM), also called the interior permanent magnet (IPM) synchronous machine, with high magnetic saliency was proven to be competitive, price-wise (Figure 8.1) [1], and superior in terms of total losses (Figure 8.2) [2] for starter/alternator automobile applications where a large constant power speed range wmax /wb > to is required The cost comparisons show the PM-RSM starter alternator system, including power electronics control, to be notably less expensive than the surface PM synchronous machine or switched reluctance machine system at the same output It is comparable with the cost of the induction machine system In terms of 8-1 © 2006 by Taylor & Francis Group, LLC 8-2 Variable Speed Generators Converter Machine $800 $700 $600 $500 $400 $300 $200 $100 IM SPM IPM VRM FIGURE 8.1 Cost comparisons for four alternators at kW and 42 Vdc total machine plus power electronics losses, the PM-RSM is slightly superior even to the surface PM synchronous machine (Figure 8.2), and notably superior to the induction machine system, all designed for the same machine volume, at 30 kW [2] It was also demonstrated that PM-RSM [2] is capable of a notably larger constant power speed range than the surface PM synchronous, or the induction, or the switched reluctance machine of the same volume In essence, both the lower cost and the wide constant power speed range are explained by the combined action of PMs and the high magnetic saliency torque to reduce the peak current for peak torque at low speed and reduce flux/torque at high speeds Starter/alternators for automobile applications are forced to operate at a constant power speed range wmax/wb > to and up to 12 to The higher the interval (without notably oversizing the machine or the converter) constant power speed range, the better This is how the PM-RSM becomes a tough competitor for electric hybrid vehicles (EHVs) The larger wmax/wb is, the smaller the PM contribution to torque In what follows, we will treat the main topological aspects, field distribution, and parameters by finite element method (FEM), lumped parameter modeling of saturated PM-RSM, core loss models, design issues for wide wmax/wb ratios, and system models for dynamics and vector flux-oriented control (FOC) and direct torque and flux control (DTFC) with and without position control feedback 5500 5000 4500 4000 (W) 3500 3000 Ind 2500 2000 Rel 1500 1000 Bru 500 0 Mix 1000 2000 3000 4000 5000 6000 7000 8000 9000 Mechanical speed (rpm) FIGURE 8.2 Loss comparisons between four starter motor-generator systems at 30 kW © 2006 by Taylor & Francis Group, LLC Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 8-3 8.2 Topologies of PM-RSM The PM-RSM is, in fact, a multilayer flux barrier and PM rotor synchronous machine — an interior multilayer PM rotor machine, in other words The standard IPM (interior PM machine) has only one PM rotor layer per pole, and the PM contribution to torque is predominant (Figure 8.3a) In PM-RSMs, the high magnetic saliency created by the multiple flux barriers in the rotor make reactance torque predominant at low speeds when highest torque is required The stator core of the PM-RSM is provided with uniform slots that host a distributed (q > 2) threephase winding with chorded coils The rotor core may be built of conventional (transverse) laminations with stamped multiple flux barriers per pole, filled with PM layers (Figure 8.3b), or from axial laminations with multiple PM layers per pole (Figure 8.3c) y (unit: mm) Stator u− v+ 35 v+ Air q axis w− d axis N M w− ag S N t Shaft ne Rotor N u+ Hole S S x 7.5 34.4 53.5 (a) (b) PM layers Axial lamination pack Nonmagnetic pole retainer Nonmagnetic spide (c) FIGURE 8.3 Rotor for permanent-magnet-assisted reluctance synchronous machine (PM-RSM): (a) standard interior permanent magnet (IPM), (b) with transverse laminations, and (c) with axial laminations © 2006 by Taylor & Francis Group, LLC 8-4 Variable Speed Generators q axis hb N d axis d axis S N N S S Optimal central ribs for mechanical ruggedness FIGURE 8.4 Mechanically acceptable flux barrier geometry The transverse lamination rotor with multiple flux barriers requires magnetic bridges to leave the lamination in one piece and provide enough mechanical resilience up to maximum design speed It turns out that mechanical speed limitations, due to centrifugal forces, basically, lead to magnetic bridges that are shorter (tangentially), while their thickness varies radially from 0.6 to (1.2) mm minimum (Figure 8.4) [3] The shorter flux bridges tend to result in larger magnetic permeance along the q axis (which is not desirable) but to larger permeance along the d axis also (which is desirable), and the Ldm to Lqm difference may be maintained acceptably large Ldm/Lqm ratios up to 10/1 may be obtained this way (Ldm and Lqm are the magnetization inductances) Placing the PMs on the bottom of the flux barriers (Figure 8.3b) has the advantage that the former are more immune to demagnetization at peak current (or torque) However, it has the disadvantage that the PM flux leakage is larger, so more PM weight is required Moreover, when the PMs are placed on the lateral part of the flux barriers the reverse is true Depending on the overload specifications and constant power speed range, the PMs may be placed either on the bottom or on the lateral parts of the flux barriers The axially laminated rotor (Figure 8.3c) [4, 5] is made of overlaid layers of axial laminations and PM flexible ribbons for each pole A nonmagnetic rotor spider sustains the poles, and a nonmagnetic pole retains them to the spider with nonmagnetic bolts There are no flux bridges between the axial lamination layers; thus, Lqm is notably smaller Also, the PM flux loss (leakage) tangentially in the rotor is smaller There are, however, three problems associated with the axially laminated anisotropic (ALA) rotor: • The manufacturing is not standard • The mechanical rigidity is not high, so the maximum peripheral speed is limited to, perhaps, 30 m/sec • The flux harmonics due to the open flux barriers produce flux pulsations in the rotor, and the q axis armature reaction space harmonics create magnetic flux perpendicular to axial lamination plane Both of these phenomena produce additional losses in the rotor, as the airgap is necessarily low to ensure high magnetic saliency: Ldm/Lqm Two of three radial slits in the rotor core (laminations) and the making of the PM of three (four) pieces axially will reduce those losses to reasonable values [4] Saliencies Ldm/Lqm = 25 under saturated conditions were obtained with a two-pole 1.5 kW machine [4] The magnetic saliency ratio Ldm /Lqm refers here only to the main flux path The leakage inductance Lsl, when included, makes the ratio Ld /Lq smaller: Ld Ldm + Lsl Ldm = ≺ Lq Lqm + Lsl Lqm © 2006 by Taylor & Francis Group, LLC (8.1) Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 8-5 Increasing the number of PM layers/pole leads to increasing the Ldm/Lqm and Ldm− Lqm but, above four PM layers (flux barriers) per half-pole, the improvements are minimal Two to four flux barriers, depending on the rotor diameter and on the number of poles, seem to suffice [6] Modification of the geometry of flux barriers, mainly their relative thickness, the shape of the flux bridges, together with the number of layers (two, three, or four), are tools to improve the Ldm/Lqm L ratio and the 1− Lqm saliency index, and thus improve performance [7] The higher the Ldm/Lqm, the dm L larger the power factor and the constant power speed range, as the torque is proportional to the 1− Lqm dm factor On the other hand, the lower the Lqm, the higher the short-circuit current So, high magnetic saliency (low Lqm /Ldm) means large short-circuit current levels 8.3 Finite Element Analysis The complex topology of the rotor, combined with the small airgap, stator slot openings, and the distributed stator windings, make a finite element analysis of flux distribution in the machine a practical way to grasp some essential knowledge about the PM-RSM capability in terms of torque for given geometry and stator magnetomotive force (mmf) 8.3.1 Flux Distribution Consider the geometry given in Table 8.1 [8] The stator–rotor structure is shown in Figure 8.5a, where the flux lines for zero stator currents are shown As expected, the flux lines “spring” perpendicular from the PMs and then spread between the flux barriers radially in the rotor [8] and then through the stator teeth The PM airgap flux density distribution in Figure 8.5b shows the presence of both multiple PM layers and the stator slot openings The average value is about 0.3 T, while the distribution is similar to that of no-load airgap flux density in induction machines Then, current of given amplitude I is injected in phase A with (−I / ) in phases B and C This way, the stator mmf distribution axis falls along the phase A axis The rotor axis d (of highest permeance) is then moved from the mmf axis by increasing mechanical angle Admitting a certain current density and slot filling factor, the slot mmf may be found without knowing the number of turns per coil in the two-layer, eight-poles, three-phase winding The calculation of torque, through FEM, is done for various maximum slot mmfs and angles, until I the maximum torque reaches the target of 140 Nm as a certain power angle δ id = tan −1( I q ) (Figure 8.6a d and Figure 8.6b) The flux lines for the peak torque conditions, with δ id = 46° (electrical degrees), are shown in Figure 8.7 The airgap flux density for the same situation, shown in Figure 8.8, evidentiates the strong influence of the stator mmf contribution (see Figure 8.4) on airgap flux density The question arises as to if, in such conditions, the PMs are not demagnetized The flux density “getting out” from the lowest barrier TABLE 8.1 Geometry of a 140 nm Peak Torque Permanent-Magnet-Assisted Reluctance Synchronous Machine (PM-RSM) Parameter Stator outer diameter Rotor outer diameter Rotor inner diameter Airgap Stack length PM parameter at 20°C © 2006 by Taylor & Francis Group, LLC Value 245.2 mm 174.2 mm 113 mm 0.4 mm 68 mm BT = 0.87 T H = 0.66 kA/m 8-6 Variable Speed Generators Flux lines 1.0363e–002 8.2894e–003 6.2162e–003 4.1430e–003 2.0698e–003 −3.3916e–006 −2.0766e–003 −4.1498e–003 −6.2230e–003 −8.2962e–003 −1.0369e–002 (a) 0.4 Bg (T) 0.3 0.2 0.1 −0.1 −0.2 −0.3 −0.4 θer (o) 20 40 80 60 100 120 140 (b) FIGURE 8.5 (a) Permanent magnet (PM) flux lines (zero stator current) and (b) airgap flux density distribution PM (Figure 8.3b) indicates clearly that the minimum flux density is 0.42 T and, thus, the PMs are safe (Figure 8.9) The computation of flux density distribution in the stator teeth, in the middle or at their bottom [8], shows that the magnetic saturation may reach 1.85 T in the teeth and 1.65 T in the back iron, in this particular design The resultant airgap flux for the maximum torque depicted in Figure 8.10 is not far from a sinusoid waveform 8.3.2 The d–q Inductances The above analysis indicates that even for rather high electric and magnetic loadings, the airgap flux distribution still keeps close to a sinusoid Consequently, the orthogonal axis (d–q) circuit model still leads, at least for preliminary design or control purposes, to practical results It goes without saying that varying the magnetic saturation has to be considered in the d–q model Also, through FEM, we may © 2006 by Taylor & Francis Group, LLC 8-7 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 150 140 130 jq Torque (N) 120 110 100 90 Is 80 70 δid 60 d 50 10 11 Rotor position (degree) 12 13 (a) (b) FIGURE 8.6 (a) The finite element method (FEM) calculated torque vs rotor position for nc I = 500 (Aturns/ coil) in phase A, and −nc I / in phases B and C ( jpeak = 17.66 A/mm2) and (b) power angle δid proceed and calculate, for given stator current, d–q current load angle, δ id : the flux linkage in phases A, B, C: Ψ A , Ψ B , Ψ C Based on these values, the d–q model flux linkages may be calculated:   2π  2π   − j  δid −  − j  δid +   2 − jδid     Ψd + j Ψq = Ψ A e + ΨB e + ΨC e  3   id = I cos δ id iq = − I sin δ id FIGURE 8.7 The flux lines for the maximum torque (140 nm) © 2006 by Taylor & Francis Group, LLC (8.2) 8-8 Variable Speed Generators 1.5 0.5 −0.5 −1 −1.5 −2 20 40 60 80 100 120 140 FIGURE 8.8 Permanent magnet (PM) airgap flux density at peak torque Now, the flux linkages Ψ dm , Ψ qm are Ψdm = Ldmid Ldm (id , iq ) = Ψqm = Lqmiq − Ψ PM Lqm (id , iq ) = Ψdm id (8.3) Ψqm + Ψ PMq iq Ψ PM is the flux produced by the PMs in phase A when aligned to rotor axis q, for zero stator currents q This way it is possible to draw, via FEM, a family of curves Ψdm (idm , iqm ), Ψqm (iqm , idm ) (Figure 8.11a and Figure 8.11b) [9] 0.9 0.8 0.7 Flux density 0.6 0.5 0.4 0.3 0.2 0.1 0 10 15 20 Length of the magnet FIGURE 8.9 Permanent magnet (PM) surface flux density at peak torque © 2006 by Taylor & Francis Group, LLC 25 30 8-9 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 0.025 0.02 0.015 0.01 Value 0.005 −0.005 −0.01 −0.015 −0.02 −0.025 20 40 60 80 Distance 100 120 140 FIGURE 8.10 The airgap flux for the maximum torque Figure 8.11a and Figure 8.11b show that the magnetic saturation is notable, especially in axis d, and though it exists, the cross-coupling magnetic saturation is not generally important [10,11] for PM-RSM For extremely high electric and magnetic loadings with peak current densities of 30 A/mm2, the situation might change; thus, direct operation with the family of d–q flux/current curves may prove necessary, via curve fitting However, for most cases, Ψ d (id ) curve suffices as Lqm = const : Ψdm = Ldm (id ) ⋅ id Ψqm = Lqm (iq ) ⋅ iq − Ψ PM Ψd,q(Vs) Ψd = Ψdm + Lsl id ′ Ψq = Ψqm + Lsl iq q (8.4) Ψdm(id, 0) 0.4 Ψdm(id, 30) 0.3 Ldm 0.2 Ψqm(0, iq) 0.1 −0.1 (a) iq = Ψqm(30, iq) iq = 30 −0.2 −5 id = Lqm id = 30 10 15 Is(A) (a) 20 25 30 IA(A) (b) FIGURE 8.11 (a) d–q axes fluxes vs current families and (b) corresponding Ldm and Lqm © 2006 by Taylor & Francis Group, LLC 8-10 Variable Speed Generators 5 FIGURE 8.12 Rotor poles with 5, flux bridges with, for example, Ldm = Ldm − β(I d − I ds ) − γ (I d − I ds )2 (8.5) Note that the q axis magnetization inductance Lqmo may depend on iq, especially at small values of currents, as the iron bridges above the flux barriers may not be fully saturated at zero stator current Also, the two-dimensional (2D) FEM analysis might not be satisfactory in predicting Lqmo or Ψ MPq , especially in short core stacks when notable axial flux leakage may occur Three-dimensional (3D) FEM is recommended to avoid the underestimation of Lqmo Also noticed on 2D FEM analyzer is the variation (pulsation) of Lqm0 with rotor position at slot frequency This phenomen is confirmed by tests 8.3.3 The Cogging Torque The torque vs rotor position developed at zero stator current is called the cogging torque The presence of stator NS slot openings and the Nr saturated flux bridges in the rotor with PMs placed in the flux barriers, is likely to create the variation of stored magnetic energy in the airgap with rotor position If we consider Ns and Nr as the number of stator and rotor “poles,” then the cogging torque fundamental number of periods per mechanical revolution Ncogging is Ncogging = smallest common multiplier of NS and NR The higher Ncogging is the smaller the cogging torque For q1 = and flux barriers per pole in the rotor and 2p1 = poles, N S = p1qm1 = ⋅ ⋅ ⋅ = 48 and N r = ⋅ p1 ⋅ = 32, N cogging = 96, which is a pretty large number The situation is not practical with the same machine and six flux barriers per pole, however, when N r = N S = 48 = N cogging With seven flux bridges per pole, however, N r = ⋅ = 56, and N cogging = ⋅ ⋅ = 336, a more favorable design is obtained (Figure 8.12) For the example in this paragraph, the cogging torque obtained through 2D FEM is shown in Figure 8.13 The very large number of periods in the cogging torque and its rather low value (percent of peak torque of 140 Nm) are evident Numerous methods to reduce cogging torque in IPM machines — with one PM piece and flux barrier per pole — were proposed Using FEM to verify them is usual [1], but analytical approaches were also introduced [12] with good results In essence, the single flux barrier radial side angle and other geometrical parameters of the latter are modified in an orderly manner (direct geometry optimization) to minimize cogging torque while limiting the electromagnetic field (emf) and main torque reductions Generalizing such methods for multiple flux barrier rotors is more complicated and still to come Usual methods to reduce cogging torque, such as stator fractionary windings (q = 3/2, for example) or stator slots skewing by up to one slot pitch are also at hand But, avoiding the undesirable stator slots © 2006 by Taylor & Francis Group, LLC 8-28 Variable Speed Generators + − + Battery Optional DC–DC converter Cf PMRSM Vdc − PWM bidirectional DC–AC inverter FIGURE 8.25 Typical pulse-width modulator (PWM) converter for permanent-magnet-assisted reluctance synchronous machine (PM-RSM) systems with voltage boost via an optional DC–DC converter (Figure 8.25) Introducing the DC–DC converter for voltage boost allows for design of the PM-RSM and the PWM converter for higher voltage, low current ratings Also, the DC voltage Vdc is made variable and the PWM converter may work extensively in the six-pulse mode when the commutation losses are reduced and the maximum modulation index is increased by 5% in comparison with standard PWM techniques (without overmodulation) There are additional losses in the DC–DC converter However, the possibility of using insulated gate bipolar transistor (IGBTs) in the higher-voltage PWM inverter leads to cost reductions in comparison with MOSFETs, but there are the additional costs of the DC–DC converter that have to be added The large battery voltage variations of ±20% or more may be absorbed by the DC–DC converter, allowing for designing the PWM inverter at least at maximum battery voltage, Vbmax The typical kVAref of the PWM three-phase inverter to deliver given active power is as follows: V I max max KVAref = (8.74) where Imax is the peak phase current value Vmax is the peak line voltage value The inverter component size Ainv is defined through the Idim = Imax and Vdim: Ainv = 6Vdim I dim (8.75) In general, Vmax < Vdim When a DC–DC converter is present, a safe value of Vmax for 600 V IGBTs would be V′max = V′dc = 400 Vdc, with V′max = Vbmin = 125 Vdc when the DC converter is missing For a 42 Vdc system, MOSFETs are to be used, and again, if a DC–DC converter is present, V′′max ≅ Vbmin (Vbmin is the minimum battery voltage.) The ratio between the inverter size and delivered mechanical power in motoring is as follows [2]: Ainv Pn = 6Vdim I dim Pn =4 Vdim KVAref ⋅ Vmax Pn (8.76) The DC–DC converter size is defined as follows: Adc −dc = 2Vdim Ib max © 2006 by Taylor & Francis Group, LLC (8.77) 8-29 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators L + − PWM DC-AC converter Cf T PM assisted RSM Battery FIGURE 8.26 H-bridge direct current (DC)–DC boost bidirectional converter with transformer and inductance (T + L) where Ibmax is the maximum battery current Adapting a total (system) efficiency ηtot yields the following: Adc −dc Vd = Pn ηtot Vb (8.78) The ratio between the inverter plus DC–DC converter to “inverter-only” size is Adc −dc + Ainv Ainv = Vb Vmax ′ + ⋅ 3ηtot Pn KVAref (8.79) The ratio P n /kVAref varies between 0.25 and 0.6, while (1 / 3ηtot ) is roughly 0.25 ÷ 0.35 For / 3ηtot = 0.34 and Pn/kVAref = 0.25, the second term in Equation 8.78 is 0.2; thus, even at Vbmin/V′max < 0.8, the total size of the DC–DC PWM converter will be lower than that of the PWM inverter at lower voltage, acting alone, and so will be the costs if the additional power switch control devices costs are small Even if the V dc = Vbmax (maximum battery voltage), it seems worth adding the DC–DC converter in ′ terms of initial silicon costs The DC–DC boost converter includes inductances for energy storage and voltage boost, but the size of the capacitive filter in front of the PWM inverter is reduced [2] and so is the current ripple in the battery A typical H-bridge DC–DC boost converter with inductance and transformer is shown in Figure 8.26 [2] Another key issue is the total loss in power electronics Converter losses are made of conduction and switching losses For an IGBT inverter leg (two switches),  ∆VR  (Pcond )leg =  VI (I )avg + (I ) RMS    Irated   (8.80) (Psw )leg = βswV I DC (I )avg The switching losses per lag in the PWM inverter for six-pulse mode (hexagonal, voltage 5% overmodulation) are as follows [2]: Psw pulse = PswHpulse sin | ϕ | PswPWM ; | ϕ |> π  − cos | ϕ |  =  PswPWM ;     π | ϕ |< (8.81) The power factor angle ϕ influences the commutation losses, as known Typical values of the above coefficients for IGBTs are VI = 0.9 V (IGBT voltage drop), ∆VR = 1.1 V (diode voltage drop), and βsw = 0.042 It was demonstrated that total losses in the power electronics with boost DC–DC converters, for 30 kW, Vbmin = 125 Vdc (Vb = 180 Vdc), Vmax = 400 V [2], are smaller than those of the PWM inverter connected © 2006 by Taylor & Francis Group, LLC 8-30 Variable Speed Generators directly to the battery terminals And, again, the PM-RSM is better in terms of total losses — machine plus power electronics — than all the other solutions for uphill or flat-terrain driving In addition, the kVAref of a PM-assisted RSM converter is smaller, and thus, the cost of power electronics is smaller 8.8 Control of PM-RSM for EHV Essentially, as for induction starter/alternators (Chapter 7), the control of PM-RSM in EHVs does torque control from zero speed and has to operate with a large constant power speed range It has to accommodate the driver’s motion expectations while observing the best possible energy transfer to and from the battery And, all this in starter (motoring) generating — for regenerative breaking and for battery recharge — and again in motoring the air conditioner or other auxiliaries during frequent engine idle stops As for the induction machine, FOC or direct torque and flux control (DTFC) are both feasible strategies Also the control system may use motion feedback (a position sensor) or may be motion sensorless (without motion feedback) The control system has to operate safely and nonhesitantly in torque control – for motoring – from zero speed So, in contrast to the induction machine, the initial rotor position has to be estimated first, in motion sensorless control Typical control schemes for FOC and DTFC with motion (position) feedback are shown in Figure 8.27 and Figure 8.28 and, respectively, in Figure 8.29 and Figure 8.30 As explained earlier, in EHV applications, torque control prevails, and thus, even for generating, the reference torque (negative) is to be used The operation modes are as follows: • • • • Starting (motoring) Regenerative braking (generating) Battery slow recharging (generation) Motoring during engine idle stop The battery state characterized here by the battery voltage only (but more complex in general) has to be considered in limiting the reference torque Also, the speed will set limits on the available torque, as the inverter output voltage is limited The torque limitation with speed may be done many ways, but from maximum torque per current (up to base speed) to maximum torque/stator flux at maximum speed, the current d–q angle may be varied as planned off-line (Figure 8.28) Only the motoring is treated in Figure 8.28 for id∗ , iq∗ calculators Expressions similar to those in Figure 8.28 may be derived for generating, but for (eventually) more flux in the machine (for given torque) The voltage decoupling is required to secure better control at + Vbattery Vbattery Reference torque T∗ calculation e operation mode PWM voltage source Position sensor (or estimated) θer θer id iq e−jq er FIGURE 8.27 Indirect current voltage vector control with synchronous current regulators © 2006 by Taylor & Francis Group, LLC PM RSM ia i b ωr ωr θer Battery Reference ∗ ∗ ∗ currents id∗, iq∗ Vd V a = Vd∗ cosqer − V q sinqer calculators, 2π 2π limiters and − Vq∗ sin qer − Vb∗ = Vd∗ cos qer − 3 synchronous Vq∗ regulators, Vc∗ = – Va∗+ Vb∗ plus voltage decoupling Speed sensor (or estimated) − Low-pass filters 8-31 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators q δi∗ δi∗ d Vd∗ iq∗ = Is∗cos δi∗ ωr Is∗ − − id Te∗ Vq∗ iq∗ = Is∗sin δi∗ − iq Te∗ = 3/2pΨPMqid+ +3/2p(Ld − Lq)idiq id∗, iq∗ calculators iq ωr Ψq = LqIq − ΨPMq Ψq id Ψd id Ψd FIGURE 8.28 Reference currents id∗ , iq∗ calculator and synchronous regulators with voltage decoupling high speeds, where the synchronous current regulators have less room for adequate control due to the influence of motion-induced voltage The presence of an absolute position sensor encoder provides for safe start from any initial position and allows for speed calculation down to less than rpm through adequate digital filtering The precalculation of optimum current angle δ i∗ as a function of speed (eventually even of reference torque) by gradually advancing it with speed, based on maximum torque/flux condition, simplifies the control notably, as the current amplitude is∗ and d–q angle δ ∗ are found unequivocally once the reference torque i and the actual speed are known A DTFC system for PM-RSM with position feedback is shown in Figure 8.29 Provided the stator flux and torque estimates are fast, robust, and precise and work from zero to maximum speed, DTFC provides for more robust control with about the same computation effort The absence of reference online * calculators of id , iq∗ and of the two vector rotators in DTFC is somewhat compensated for by the occurrence of the stator flux and torque estimator Vbattery Reference Te∗ torque calculation, operation mode + − Battery 1, 0, −1 Table of optional switching (see Chapter 7) − 1, −1 Vdc PWM voltage source converter PM RSM θr − Ψ s∗ V θΨs(1, 2, 6) dc Ψs Stator flux and torque estimator ⎢ r⎢ ω ωr Te ia ib p θer d/dt plus filter ωr θΨs FIGURE 8.29 Direct torque and flux control (DTFC) of permanent-magnet-assisted reluctance synchronous machine (PM-RSM) with position feedback © 2006 by Taylor & Francis Group, LLC 8-32 Variable Speed Generators id  Ψss Vs − αβ − I s∗ Ψd dq iq = (Ψq + ΨPMq)/Lqo dq αβ ss I − Rs Is θer Kp Ki  Ψss  Te Ι s∗ FIGURE 8.30 Combined voltage-current model observers for stator flux and torque Stator flux estimation, with position feedback, is straightforward, though many schemes may, in principle, be applied, from model-reference adaptive-system (MRAS) to Kalman filters and so forth A combined voltage-current model state observer is shown in Figure 8.30 In essence, the voltage model is corrected through the current estimator’s error: s ∫ Ψs = (V s − Rs I s + Vcomp )dt  K  ˆ Vcomp =  K p + i  I s s − I s s s   ( ) (8.82) The magnetic saturation influence in axis d is considered The design of the PI controller is done such that at low speeds, the current model acts practically alone Typical values of Kp and KI are Kp = 22 to 33 rad/sec, Ki = 40 to 90 (rad/sec)2 Inverter nonlinearities occur at very low speed, but as the current model is dominant, they not have a very important influence 8.9 State Observers without Signal Injection for Motion Sensorless Control In the absence of position feedback, in indirect FOC schemes, only the rotor position θer and speed ωr have to be estimated [4] They have to be used, however, two times for vector rotation and once in the voltage decoupler (ωr) The problem is that large errors, due to slow observer response or low immunity to machine parameter detuning, may notably influence the field orientation, and the fast, precise, torque control is lost In contrast, for DTFC schemes, rotor position is not required in the control, but speed ωr , the stator flux Ψs , and torque Te have to be estimated The stator flux estimator, in general, requires the estimated rotor position However, its influence is notable only at low speeds, when the current model is predominant (Figure 8.30) A straightforward way to calculate the rotor position for the flux observer purposes would be as follows (Figure 8.31a and Figure 8.31b): ˆ ˆ θ er = θ Ψs + δ Ψs , for motoring ˆ θ er = θ Ψs − δ Ψs –π , for generating © 2006 by Taylor & Francis Group, LLC (8.83) 8-33 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators jq jq Id < Iq > iq ΨPMq Ldid iq id θΨs δΨs jLqoiq Is Is jLqoiq Id > Iq > lq d Ldid δΨs θer ΨPMq Ψs θer θΨs Ψs d Ph (fix ase a ed ) Ph (fix ase a ed ) (a) (b) FIGURE 8.31 Rotor position θer in relation to δψs and θψs: (a) generating and (b) motoring  Ψs  θ Ψ = sin −1  sα  ; Ψd = Ψs cos δ Ψs  | Ψ | S  s  Te = Ψq = Ψs sin δ Ψs (8.84) Ψ s sinδ Ψ  Ψ cosδ  S Ψs p  Ψ PMq + (Ld (Ψ d ) − Lq )  s  Lq0  Ld (Ψ d ) (8.85) The stator flux and torque observer in Figure 8.30 may be augmented with Equation 8.83 through Equation 8.85 to include the rotor position θer calculator Equation 8.85 may be simplified, as δ Ψs is, in general, a small angle (below 30° in most cases), and cos δΨs ≈ 1: ˆ   ˆ −2 | Te | Ld (Ψ S ) Ψ PMq Ld (Ψs )  ˆ |δ Ψs | ≈  + ˆ  3p Lq  Ψs Ψs   Ld ( Ψs ) Lq −1 (8.86) This way, the online computation effort is reduced drastically Such a position estimator θer (calculator) is acceptable for DTFC schemes, as θer appears only in the flux observer This is not so for FOC schemes, where θer is crucial for field orientation Still, the speed has to be estimated Again, as precise speed control is not needed, the estimated speed is used for adjusting the reference flux Ψs∗ and reference torque Te∗ At low speeds, this information is not important, as Ψs∗ generally remains constant To a first approximation, then, the steady-state speed ˆ estimation may be adopted That is, the stator flux vector speed is used instead of ω r : ˆ ˆ ω Ψ ≈ ωr = S Ψsβ (k)Ψsα (k − 1) − Ψsα (k)Ψsβ (k − 1) Tsample (Ψs2α (k) + Ψs2β (k)) (8.87) After low-pass filtration, such a signal should be enough for torque and flux references So, for sensorless DTFC of PM-RSM, with torque (not speed) control at zero speed, the flux and torque estimators need rotor position and speed calculators that are fast but not so accurate The question remains if such a fundamental excitation (no signal injection) state observer can provide nonhesitant start and fast torque control at zero speed At least for the induction machines, it did Many other state observers for FOC or DTFC of IPM synchronous machines without signal injection were proposed Luenberger, MRAS, and Kalman filter observers all use the stator voltage vector equation © 2006 by Taylor & Francis Group, LLC 8-34 Variable Speed Generators (voltage model) and the current model, and the flux current relationship in d–q rotor coordinates Sliding mode such observers were proven to yield good stator flux rotor position and speed estimation down to very low speeds (a few rpm) [20] However, robust fast torque sensorless control of PM-RSM at zero speed, without signal injection, is still due to be proven by tests And, this is so due to the need to estimate first, at zero speed, the initial rotor position This is how the signal injection state observers for PM-RSM come into play 8.10 Signal Injection Rotor Position Observers Signal injection state observers are based on machine magnetic saliency tracking Back-emf methods not use signal injection but cannot work at very low speeds, or at zero speed These methods are used to detect rotor position, and then, from the latter, the rotor speed is estimated through adequate filtering Saliency tracking by signal injection works well from zero speed, but it limits available DC link voltage at high speeds A combination of the saliency tracking — to 10% maximum speed — and back-emf tracking above 10% of maximum speed was recently proven experimentally as being very good from to 5000 rpm in 70 kW IPM synchronous machine control [21] with ±100% torque and 150 msec ramp control at 100 rpm and at 5000 rpm Saliency tracking methods are used to estimate absolute rotor position A voltage (current) signal at a carrier frequency ωc above 500 Hz is injected in rotor d–q coordinates in the FOC The response in current is used to track the spatial saliency and thus the rotor position The injected signals (in voltage) are of the following form: c Vdq = Vc cos ω c t − jVc sin ω c t (8.88) The machine response in current, separated through adequate filtering, is as follows: c I dq = I p sin ω i t − In cos(hθ er − ω i t ) − j(I p cos ω i t − In sin(hθ er − ω i t )) (8.89) Ip and In are positive and negative sequence carrier currents, while h is the order of the saliency spatial harmonic; θer is the rotor position Only the negative sequence current contains the rotor position information Also, in general, only one spatial harmonic (h) is considered The negative sequence current is processed through heterodyning to produce a signal that is proportional to the rotor position error This ∆θer (error) signal is then used as input to a Luenberger observer that produces parameter-insensitive zero lag position and speed estimates [22–24] For the back-emf methods, used for high speeds, the method in Section 8.9 is typical The basic structure of such a hybrid sensorless FOC, with saliency plus back-emf position and speed tracking, is shown in Figure 8.32 [21] The switching from low-speed position estimation to high-speed position estimation is done when the two have the same output, around 10 to 15% of maximum speed, to leave room for full voltage utilization by the voltage source inverter Position estimation results at 100 rpm and at 5000 rpm, for a 70 kW IPM-SM, obtained with the above combined control method, is shown in Figure 8.33 and Figure 8.34 [21] Torque ranging of ±100% is experienced with apparently flowless position estimation Still, for safe torque control at zero speed, the initial rotor position is required This is not directly possible with the above method 8.11 Initial and Low Speed Rotor Position Tracking A simple way to detect initial rotor position is to use three proximity Hall sensors placed in the axes of the three phases, to detect the PM flux position The resolution of such a coarse position tracker is only 180/3 = 60° (electrical) For DTFC, such an error may be acceptable, as the method still indicates correctly © 2006 by Taylor & Francis Group, LLC 8-35 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators Vbattery Vbattery Te∗ calculator Te∗ Synchronous current regulators, Id∗, Iq∗ references and limiters considering flux weakening Vd∗ Vα∗ e jq er Vq∗ Vdc PWM voltage source inverter Vβ∗ PMRSM Vα∗ Vβ∗ Vqc ia wr  ib Vbattery LPF Iq∗ iα Id∗ iβ Vab Vbc −jq er e  High frequency qerlow injection method (for low speed) qer  qerhigh  Back emf rotor position tracking wr  FIGURE 8.32 Sensorless flux-oriented control (FOC) of permanent-magnet-assisted reluctance synchronous machine (PM-RSM) with signal injection plus back electromagnetic force (emf) rotor position estimation the first voltage vector in the table of optimal switchings to be triggered in the inverter For FOC, better precision is required to secure safe smooth torque for starting The additional wiring for the Hall sensors may lead to failure Pulse signal [25] or sinusoidal carrier signal [23–29] methods were proposed in the last decade for initial position tracking in IPM-SMs The slight magnetic saturation due to the PM “North Pole” presence is used to find the PM polarity and, thus, settle for the actual rotor initial position (Figure 8.35) Consequently, magnetic saturation θact θest Tcmd Tfdbk FIGURE 8.33 Dynamic performance of injection at 100 rpm (Adapted from M Patel, T O’Meara, J Nagashinia, and R.D Lorenz, Encoderless IPM drive system for EH-HEV propulsion applications, Record of EPE-2001, Graz, Austria, 2001.) © 2006 by Taylor & Francis Group, LLC 8-36 Variable Speed Generators Vsds θact Vsds_mod θest_high FIGURE 8.34 Comparison of actual and estimated rotor position at 5000 rpm in six-step mode under full load condition using BEMF method (Adapted from M Patel, T O’Meara, J Nagashinia, and R.D Lorenz, Encoderless IPM drive system for EH-HEV propulsion applications, Record of EPE-2001, Graz, Austria, 2001.) has to be considered in the PM-RSM model The voltage model vector equation of PM-RSM is as follows: VS = RS iS + dΨ r + jω r Ψ S dt (8.90) Ψ S = Ψ d + jΨ q (8.91) Magnetic saturation is considered separately for the two axes: id + jiq = Rd λd + Rd1λd + Rd λd + j[Rq0 (λq − λ PMq ) + Rq1(λq − λ PMq )2 ] d d Phase a Phase a N (8.92) S S jq N jq (a) Demagnetization (b) Magnetization FIGURE 8.35 Magnetic saturation in the q axis of a permanent-magnet-assisted reluctance synchronous machine (PM-RSM) © 2006 by Taylor & Francis Group, LLC 8-37 Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 0.2 Current (A) 0.3 101 Current (A) 102 100 10–1 10–2 2θc idsc_θr 2θc iqsc_θr 0.1 –0.1 –0.2 10–3 –1000 –500 500 –0.3 1000 90 180 270 360 FIGURE 8.36 Measured carrier current spectrum Only two terms were retained in axis q, as the magnetic saturation here is less important, as demonstrated earlier in this chapter Along axis d, magnetic saturation is heavy for the large starting torque The magnetic saturation functions are mere qualitative, used to discriminate the machine current response waveform when a sinusoidal voltage signal injection is applied A sinusoidal voltage injection method is illustrated in what follows [30] c The injected signal Vαβ in stator coordinates is as follows: c Vαβ = Vc e jω i t c c Vdq = Vαβ e − jθer (8.93) In rotor coordinates, (8.94) Neglecting the resistive voltage drop, ∫ Ψc = Vdq c dt dq (8.95) Then, making use of Equation 8.92, the injected currents in stator coordinates are as follows: I c αβ = I cp1e  π j ωc t −  2  + I cn1e j ( −ω c t + 2θer +φ1n ) + I cp e j ( 2ω c t −θer +φ2 p ) + I cn e j ( −2ω c t + 3θer +φ2n ) (8.96) The first and second time harmonic components are illustrated in Equation 8.96 Only the last three terms contain rotor position information at the second, first, and, respectively, third spatial harmonic The measured carrier current spectrum at standstill in stator coordinates (Equation 8.96) is shown in Figure 8.36 [30] The negative sequence first time harmonic (second-space harmonic) current — the second term in Equation 8.96 — contains the largest signal and seems to be most appropriate for initial position detection In Reference [30], the Icn1 and Icn2 terms in Equation 8.96 are used to estimate the position ˆ error θ er − θ er , after frame transformations from stationary to ωc and 2ωc reference frame speeds, and after taking their dot product: −θ I dq 2cθ = I cn1e j ( 2θer +φ1n ) er ∗−θ −2θ ; I dq3θc = I cn 2e −2θ s I dqθ = I dq 2θc ⋅ I dq3θc = I cn1 I cn 2e er © 2006 by Taylor & Francis Group, LLC er j (3θer +φ2 n ) er er j (θer +φ1n −φ2 n ) (8.97) (8.98) 8-38 Variable Speed Generators kio s iabs e jqc –q idq c o s idqer s idqqer × Te∗ bo s e j2qc –2q idq c × s iqqer s qm p wm J ko wr Tload +j qer e j(qer + fn1 − fn2) p qer (Unit vector) FIGURE 8.37 Fundamental rotor position and speed tracking observer A first method to extract the rotor position error from Equation 8.98 is by the vector cross-product with its unit vector: s ˆ ˆ ∗ ε = UI dqsθ × I dqθ = sin(θ er − θ er ) er (8.99) er 360 240 Spatial STO w/polarity 120 −120 Fundamental RPTO Fundamental RPTO 360 240 Spatial STO w/polarity 120 0 480 360 240 0.005 0.01 0.015 0.02 0.025 0.03 Time (sec) Case 3: 240° initial position FIGURE 8.38 Estimated initial electrical rotor position © 2006 by Taylor & Francis Group, LLC Spatial STO w/polarity 120 Fundamental RPTO −120 0.005 0.01 0.015 0.02 0.025 0.03 Time (sec) Case 1: 60° initial position 480 −120 Electrical rotor position (deg) 480 0.005 0.01 0.015 0.02 0.025 0.03 Time (sec) Case 2: 120° initial position Electrical rotor position (deg) Electrical rotor position (deg) Electrical rotor position (deg) No magnet polarity detection is required [30] The block diagram of the initial position tracking observer, based on this principle, is shown in Figure 8.37 Experimental results in Reference [30] show remarkable initial position tracking precision at 60°, 120°, 240°, and 300° (electrical), with a convergence time of 25 msec, for fc = 500 Hz (Figure 8.38) Even faster convergence (10 msec) is reported for a derivative method with additional magnet polarity compensation (Figure 8.38) 480 Fundamental RPTO 360 240 Spatial STO w/polarity 120 −120 0.005 0.01 0.015 0.02 0.025 0.03 Time (sec) Case 4: 300° initial position Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 8-39 As the above method can be applied as it is at small speeds also, it may be used successfully in combination with the back-emf method for FOC (Figure 8.32 to cover the entire speed range from standstill) The same procedure may be used in DTFC to detect θer for the use in the flux observer only (Figure 8.30) 8.12 Summary • A high magnetic saliency (Ld /Lq > 3) RSM with multilayer interior PMs per rotor poles in axis q is called PM-assisted RSM or PM-RSM It may also be called a special interior PM synchronous machine • The reluctance torque is predominant in comparison with the PM interaction torque, for peak value • Even low remnant flux density PMs (Br < 0.8 T) and, thus, lower-cost PMs may be used • In automotive applications, typical specifications ask for high start torque up to base speed ωb , and then a wide constant power speed range F = ωmax /ωb > 4/1 is required • The unique combination of reluctance and PM interaction torque makes the PM-RSM particularly suitable for a wide constant power speed range both in terms of system costs and losses • Typical rotor topologies contain two to four (five) flux barriers per half pole, which contains parallelepiped-shaped moderate (low)-cost PMs The rotor core is made of conventional laminations The saliency ratio Ldm/Lqm ≈ to 10, but it greatly varies with magnetic saturation level • Each flux barrier ends toward airgap with a flux bridge The bridge thickness varies between 0.5 to 1.5 mm The smaller the bridge, the better, in terms of rotor saliency Ldm /Lqm, but, alternatively, the flux bridge thickness and length are limited by the mechanical stress allowed before rotor deformation at maximum speed and torque occurred • The total saliency is Ld /Lq = to for PM-RSM below 100 kW (peak torque below 400 Nm) when two to four flux barriers per half-pole are used The stator windings leakage inductance reduces Ld /Lq to values smaller than Ldm /Lqm • FEM direct geometrical optimization of the rotor pole structure may lead to a uniform distribution of PM flux density in the airgap, that is, to a rather sinusoidal emf for a distributed stator winding with q = 2,3 slots per pole and phase • Also, a prime number of flux bridges per pole of five or seven, leads to low cogging torque and pulsating torque with sinusoidal currents, even without stator (rotor) skewing • Even for heavy saturation levels, the airgap resultant flux linkage per phase is sinusoidal if magnetic saturation is uniform in the stator and rotor teeth and yokes • FEM analysis brings out the fact that magnetic saturation moves the maximum torque for given (high) current toward smaller id and larger iq • The sinusoidal airgap flux per phase under load allows for full usage of d–q models of PM-RSM for parameter, steady-state, transient, and control performance estimation • If FEM analysis shows that magnetic saturation in axis q (where the PMs are located) is almost negligible, while it is important in axis d, especially for high torque operation; cross-coupling magnetic saturation may, thus, be neglected in many practical cases Saturation in axis d is accounted for by a nonlinear id (Ψd) function • Core losses in the PM-RSM occur both in the stator and the rotor Only space harmonics in the airgap total flux distribution produce rotor core losses under steady state Stator current time harmonics produce core losses both in the stator and the rotor Both space and time harmonics of the airgap field produce eddy currents in the PMs on the rotor, especially at high speeds • From FEM static field analysis, the core losses may be calculated An equivalent, slightly frequencydependent, core resistance RC is defined for use in the d–q model • The d–q model flux linkages Ψd = Ld(id)id, Ψq = Lqiq − ΨPMq lead to a resultant torque that is proportional to id When torque changes sign (from motoring to generating), it is id rather than iq that changes sign © 2006 by Taylor & Francis Group, LLC 8-40 Variable Speed Generators • The PMs in axis q produce a flux that opposes Lqiq; that is, a demagnetizing armature reaction occurs The current iq should not change polarity • The PMs in axis q contribute to additional torque for less Ψq flux and, thus, to high power factor in the machine • Generator no-load with nonzero core losses makes the d–q output current id = iq= but the interior currents i0d, i0q ≠ • With zero current losses (RC = ∞), all d-q currents in the d–q model at no load are zero, and Vd00 = ωrΨPMq and Vq00 = • The symmetrical steady-state short-circuit current when RS ≠ 0, RC ≠ ∞ has two components idsc3 and iqsc3 and a corresponding torque With zero losses, the ideal symmetrical short-circuit current isc3 = iqs0 = ΨPMq /Lq • In most wide constant power speed range designs, ΨPMq = LqIsrated and, thus, symmetrical shortcircuit is acceptable • Unsymmetrical short-circuit leads to larger than isc currents with DC components that have to be treated, eventually, through quick, intentional, triggering of all power switches in the inverter to degenerate in symmetrical short-circuit This way, the inverter is protected • The design of PM-RSM for a wide speed range has to compromise machine (torque) and inverter (current) oversizing tover, iover After smart normalization, only ΨPMq and Ld /Lq in P.U remain as independent variables In essence, design close to ΨPMq /Lq ≈ in (P.U.) leads to wide constant power speed range • With respect to base speed ωb (full torque at full voltage for maximum torque per current), the minimum speed ωmin may be chosen either above or under it For given constant power speed range F, choosing a ωmin/ωb > smaller machine and some inverter oversizing are required, but the emf at maximum speed limitation at 150% rules out such a situation with designs for ΨPMq / Lq ≈ P.U Also, the full voltage at ωb < ωmin may lead to current regulation saturation For ωmin/ ωb < 1, full machine utilization is reached, but inverter current oversizing is larger • Uncontrolled generation (UCG) occurs even when the speed decreases to ωUCG, below that for which ωrΨPMq < Vb and the PWM inverter power switches are turned off and diodes act alone To avoid UCG, the maximum speed ωmax should be lower than ωUCG: ω max < ωUCG = Ld Lq Ψ PMq −1 ( ) Ld Lq ∗ ω b ; Ψ PMq in P.U • It turns out that, for F > 4, only for very small Ψ PMq values and low Ld/Lq ratios, UCG may be eliminated Essentially, to avoid an unpractical design, UCG has to be eliminated through control (protection) means • For EHVs, the PM-RSM starter/alternator is connected to the battery through a PWM inverter As the battery voltage varies with ±25%, it turns out that a voltage booster, through a DC–DC converter, may be beneficial Even if the voltage booster acts from Vbmin to Vbmax of battery, the total ratings and silicon costs of a DC–DC converter plus PWM inverter are smaller than those for the inverter alone at Vbmin Moreover, the total system losses in the machine plus converters are smaller with a DC voltage booster • In EHVs, torque, rather than speed, control is required both for motoring and generating • FOC and DTFC strategies are feasible • The control may be performed with or without a position encoder ∗ • The control has to produce first reference d–q currents i d , i ∗ vs torque and speed functions for q motoring and generating in FOC, or reference flux vs speed and torque for DTFC • Varying the d–q current angle with speed from maximum torque per current criterion, below base speed, to maximum torque per flux criterion, at maximum speed, seems a good way for FOC © 2006 by Taylor & Francis Group, LLC Permanent-Magnet-Assisted Reluctance Synchronous Starter/Alternators 8-41 • For DTFC, a flux and torque observer is required • The position feedback is used two times for vector rotation in FOC, while only in the flux observer for DTFC For motion-sensorless control, position observers, capable of working from zero speed, are required • Initial position estimation is required with FOC, for safe starting • Signal injection rotor position observers were proven capable of safe zero and low speed good performance In combination with back-emf rotor motion observers, the whole speed range is covered for FOC [31, 32] • For DTFC, as only torque control at zero speed is required, even a rotor position and flux observer without signal injection may be adequate for the whole speed range, with initial position estimation References E.C Lovelace, T.M Jahns, J.L Kirtley Jr., and J.H Lang, An interior PM starter/alternator for automotive applications, Record of ICEM-1998, Istanbul, vol 3, 1998, pp 1802–1808 A Vagati, A Fratta, P Gugliehmi, G Franchi, and F Villata, Comparisons of AC motor based drives for electric vehicle application, Record of PCIM-1999, Europe Vol., Intelligent Motion, 1999, pp 173–181 E.C Lovelace, T.M Jahns, T.A Keim, and J.H Lang, Mechanical design considerations for conventionally-laminated high-speed interior PM synchronous machine rotors, Record of IEEE–IEMDC-2001, 2001, pp 163–169 I Boldea, Reluctance Synchronous Machines and Drives, Oxford University Press, Oxford, 1996 W.L Soong, D.A Staton, and T.J.E Miller, Design of new axially-laminated interior permanent magnet motor, Record of IEE–IAS, 1993 Annual Meeting, 1993, pp 27–36 Y Honda, Rotor design optimization of a multilayer interior PM synchronous motor, Proc IEE, EPA-145, 2, 1998, pp 119–124 A Vagati, A Canova, M Chiampi, M Pastorelli, and M Repeto, Design refinement of synchronous reluctance motors through finite element analysis, IEEE Trans., IA-36, 4, 2000, pp 1094–1102 I Boldea, L Tutelea, and C.I Pitic, PM assisted reluctance synchronous motor/generator (PMRSM) for mild hybrid vehicle, Record of OPTIM-2002, Poiana Brasov, Romania, 2002, pp 383–388 P Guglielmi, G.M Pellegrino, G Griffero, S Mieddu, G Girando, and A Vagati, Conversion concept for advanced autonomy and reliability scooter, Record of IEEE–IECON, 2003, pp 2883–2888 10 E.C Lovelace, T Jahns, T Keim, J Lang, D Wentzloff, F Leonardi, J Miller, and P McCleer, Design and experimental verification of a direct-drive interior PM synchronous machine using a saturable parameter model, Record of IEEE–IAS-2002 Annual Meeting, 2002 11 D.H Kim, I.H Park, J.H Lee, and C.E Kim, Optimal shape design of iron core to reduce cogging torque of IPM motor, IEEE Trans., MAG-39, 3, 2003, pp 1456–1459 12 G.H Kang, J.P Hong, and G.T Kim, Analysis of cogging torque in interior permanent magnet motor by analytical method, J KIEE, 11-B, 1, 2001, pp 1–8 13 K Yamazaki, Torque and efficiency calculation of an interior permanent magnet motor considering harmonic iron losses of both stator and rotor, IEEE Trans., MAG-39, 3, 2003, pp 1460–1463 14 T.A Jahns, Component rating requirements for vehicle constant power operation of IPM synchronous machine drives, Record of IEEE–IAS-2000, Annual Meeting, Rome, 2000, pp 1697–1704 15 R.F Schiferl, and T.A Lipo, Power capabilities of salient pole permanent magnet synchronous motor variable speed applications, IEEE Trans., IA-26, 1, 1990, pp 115–123 16 B.A Welchko, T.A Jahns, W.C Long, and J.M Nagashima, IPM synchronous machine drive response to symmetrical and asymmetrical shortcircuit faults, IEEE Trans., EC-28, 2, 2003, pp 291–298 17 T.M Jahns, Uncontrolled generator operation of interior PM synchronous machine following highspeed inverter shutdown, Record of IEEE–IAS, 1998 © 2006 by Taylor & Francis Group, LLC 8-42 Variable Speed Generators 18 W.L Soong, N Ertugrul, E.C Lovelace, and T.M Jahns, Investigation of interior permanent magnet off-set coupled automotive integrated starter/alternator, Record of IEEE–IAS-2001, Annual Meeting, 2001 19 I Boldea, L Ianosi, and F Blaabjerg, A modified direct torque control (DTC) of reluctance synchronous motor sensorless drive, EMPS J., 28, 1, 2000, pp 115–128 20 G.D Andreescu, Robust sliding mode based observer for sensorless control of PMSM drives, Record of EPE–PEMC-1998, vol 6, Prague, 1998, pp 172–177 21 M Patel, T O’Meara, J Nagashinia, and R.D Lorenz, Encoderless IPM drive system for EH-HEV propulsion applications, Record of EPE-2001, Graz, Austria, 2001 22 M.M Degner, and R.D Lorenz, Wide band width flux position and velocity estimation in AC machines at any speed (including zero) using high multiple saliences, Record of EPE-1997, Trondheim, Norway, 1997, pp 1530–1535 23 M.M Corely, and R.D Lorenz, Rotor position and velocity estimation for a permanent magnet synchronous machine at standstill and high speed, IEEE Trans., IA-34, 4, 1998, pp 784–789 24 T Aihara, A Tobu, T Yanase, A Mashimoto, and K Endo, Sensorless torque control of salient pole synchronous motor at zero speed operation, IEEE Trans., PE-14, 1, 1999, pp 202–208 25 M Schroedl, Sensorless control of AC machines at low speed and standstill based on the INFORM method, Record of IEEE–IAS-1996 Meeting, vol 1, 1996, pp 270–277 26 A Consoli, G Scarcella, and A Testa, Sensorless control of PM synchronous motors at zero speed, Record of IEEE–IAS-1999 Annual Meeting, vol 2, 1999, pp 1033–1040 27 T Noguchi, K Yamada, S Kondo, and I Takahashi, Initial rotor position estimation of sensorless PM synchronous motor with no sensitivity to armature resistance, IEEE Trans., IE-45, 1, 1998, pp 118–125 28 D.W Chung, J.K Kang, and S.K Sul, Initial rotor position detection of PMSM at standstill without rotational transducer, Record of IEEE–IEMDC-1999, 1999, pp 785–787 29 J.I Ha, K Ide, T Sawa, and S.K Sul, Sensorless position control and initial position estimation of an interior permanent magnet motor, Record of IEEE–IAS-2001, 2001, pp 2607–2613 30 H Kim, K.K Huh, H Harke, J Wai, R.D Lorenz, and T Jahns, Initial rotor position estimation for an integrated starter alternator IPM synchronous machine, Record of EPE-2003, Toulouse, France, 2003 31 Y Yeong, R.D Lorenz, T.M Jahns, and S.K Sul, Initial rotor position estimation of interior PMSM using carrier-frequency injection methods, Record of IEEE–IEMDC-2003, vol 2, 2001, pp 1218–1223 32 M Linke, R Kennel, and J Holtz, Sensorless speed and position control of synchronous machines using alternating carrier injection, Record of IEEE–IEMDC-2003, vol 2, 2003, pp 1211–1217 © 2006 by Taylor & Francis Group, LLC ... 0.8 0.6 Torque 0.4 0.2 Base speed FIGURE 8.20 Torque, power, and voltage vs speed © 2006 by Taylor & Francis Group, LLC Speed (P.U.) 10 w max w r wb wb 8-22 Variable Speed Generators In general,... motoring, in the same cases The typical torque /speed and voltage /speed envelopes are given in Figure 8.20 The base speed ωb is defined as the maximum speed for which the peak (starting) torque is... Still, the speed has to be estimated Again, as precise speed control is not needed, the estimated speed is used for adjusting the reference flux Ψs∗ and reference torque Te∗ At low speeds, this